# Safe Learning of Quadrotor Dynamics Using Barrier Certificates

arXiv: https://arxiv.org/abs/1710.05472 · HTML: https://mlsanity.com/paper/1710.05472/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2017.

## Built on by (most cited first, 30 of 35)

- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Learning Safe Multi-Agent Control with Decentralized Neural Barrier Certificates](https://mlsanity.com/paper/2101.05436/) (2021)
- [safe-control-gym: a Unified Benchmark Suite for Safe Learning-based Control and Reinforcement Learning in Robotics](https://mlsanity.com/paper/2109.06325/) (2021)
- [Safe Reinforcement Learning for Legged Locomotion](https://mlsanity.com/paper/2203.02638/) (2022)
- [Learning Robust Output Control Barrier Functions from Safe Expert Demonstrations](https://mlsanity.com/paper/2111.09971/) (2021)
- [Active Learning of Discrete-Time Dynamics for Uncertainty-Aware Model Predictive Control](https://mlsanity.com/paper/2210.12583/) (2022)
- [BarrierNet: A Safety-Guaranteed Layer for Neural Networks](https://mlsanity.com/paper/2111.11277/) (2021)
- [Differentiable Control Barrier Functions for Vision-based End-to-End Autonomous Driving](https://mlsanity.com/paper/2203.02401/) (2022)
- [Data-Driven Distributionally Robust Safety Verification Using Barrier Certificates and Conditional Mean Embeddings](https://mlsanity.com/paper/2403.10497/) (2024)
- [SkyJEPA: Learning Long-Horizon World Models for Zero-Shot Sim-to-Real Control of Quadrotors](https://mlsanity.com/paper/2606.23444/) (2026)
- [SO(2)-Equivariant Downwash Models for Close Proximity Flight](https://mlsanity.com/paper/2305.18983/) (2023)
- [DroneDiffusion: Robust Quadrotor Dynamics Learning with Diffusion Models](https://mlsanity.com/paper/2409.11292/) (2024)
- [Provably Correct Training of Neural Network Controllers Using Reachability Analysis](https://mlsanity.com/paper/2102.10806/) (2021)
- [Lightweight Distributed Gaussian Process Regression for Online Machine Learning](https://mlsanity.com/paper/2105.04738/) (2021)
- [Computationally and Sample Efficient Safe Reinforcement Learning Using Adaptive Conformal Prediction](https://mlsanity.com/paper/2503.17678/) (2025)
- [Model Free Barrier Functions via Implicit Evading Maneuvers](https://mlsanity.com/paper/2107.12871/) (2021)
- [Decentralized Safe Multi-agent Stochastic Optimal Control using Deep FBSDEs and ADMM](https://mlsanity.com/paper/2202.10658/) (2022)
- [Sample-efficient Safe Learning for Online Nonlinear Control with Control Barrier Functions](https://mlsanity.com/paper/2207.14419/) (2022)
- [A Joint Imitation-Reinforcement Learning Framework for Reduced Baseline Regret](https://mlsanity.com/paper/2209.09446/) (2022)
- [Learning to Navigate in Turbulent Flows with Aerial Robot Swarms: A Cooperative Deep Reinforcement Learning Approach](https://mlsanity.com/paper/2306.04781/) (2023)
- [Safe Reinforcement Learning for Power System Control: A Review](https://mlsanity.com/paper/2407.00681/) (2024)
- [Estimating Control Barriers from Offline Data](https://mlsanity.com/paper/2503.10641/) (2025)
- [Exact Recovery for System Identification with More Corrupt Data than Clean Data](https://mlsanity.com/paper/2305.10506/) (2023)
- [Safety-Critical Learning of Robot Control with Temporal Logic Specifications](https://mlsanity.com/paper/2109.02791/) (2021)
- [Barrier Certified Safety Learning Control: When Sum-of-Square Programming Meets Reinforcement Learning](https://mlsanity.com/paper/2206.07915/) (2022)
- [Machine Learning for Smart and Energy-Efficient Buildings](https://mlsanity.com/paper/2211.14889/) (2022)
- [EnergyShield: Provably-Safe Offloading of Neural Network Controllers for Energy Efficiency](https://mlsanity.com/paper/2302.06572/) (2023)
- [Real-Time Adaptive Safety-Critical Control with Gaussian Processes in High-Order Uncertain Models](https://mlsanity.com/paper/2402.18946/) (2024)
- [Learning to Control an Unstable System with One Minute of Data: Leveraging Gaussian Process Differentiation in Predictive Control](https://mlsanity.com/paper/2103.04548/) (2021)
- [ProBF: Learning Probabilistic Safety Certificates with Barrier Functions](https://mlsanity.com/paper/2112.12210/) (2021)

## Abstract (arXiv)

To effectively control complex dynamical systems, accurate nonlinear models are typically needed. However, these models are not always known. In this paper, we present a data-driven approach based on Gaussian processes that learns models of quadrotors operating in partially unknown environments. What makes this challenging is that if the learning process is not carefully controlled, the system will go unstable, i.e., the quadcopter will crash. To this end, barrier certificates are employed for safe learning. The barrier certificates establish a non-conservative forward invariant safe region, in which high probability safety guarantees are provided based on the statistics of the Gaussian Process. A learning controller is designed to efficiently explore those uncertain states and expand the barrier certified safe region based on an adaptive sampling scheme. In addition, a recursive Gaussian Process prediction method is developed to learn the complex quadrotor dynamics in real-time. Simulation results are provided to demonstrate the effectiveness of the proposed approach.